Asymmetric fibre optic couplers and their fabrication

ABSTRACT

An asymmetric multi-mode fibre optic coupler is assembled from two or more multi-mode optical fibres of different core and cladding diameters but substantially equal cladding refractive indices. The fibres are selected so as to have substantially equal effective refractive indices for their respective highest-order cladding modes, at least in the fabricated coupler.

BACKGROUND OF THE INVENTION

This invention relates generally to fiber optic couplers, and isconcerned in particular with the fabrication of asymmetric fiber opticcouplers

The simple symmetric fiber optic coupler, in which input light at anybranch is split substantially equally between output branches, haslittle practical application to linear fiber optic buses and networkssince only a trivial number of taps are possible before optical signalstrengths become impracticably small. Larger linear fiber optic networksrequire asymmetric couplers in which tap-off coupling is substantiallyless than half, but tap-on coupling is much greater than the tap-offcoupling. In the context of this specification, the terms "asymmetriccoupler" and "asymmetric coupling" refer to coupling asymmetry of thiskind. Such a requirement arises, for example, in networks where eachcomponent tied to a bus includes both an optical transmitter and anoptical receiver, the receiver tapping the bus in front of the tap forthe transmitter.

It has been proposed that asymmetric couplers having, e.g. a throughputpower coupling factor, e.g. on a bus, of 95 and a tap-off couplingfactor of 1.5%, might be fabricated by employing conventional techniquesto merge two optical fibers of substantially different diameters or bysimply reducing the nominal coupling factor of two similar fibers. Theresultant couplers are satisfactory for single-mode applications, e.g.in basic telecommunication systems, but unacceptable for multi-modeoperation because of significant power losses and the restrictedproportion of modes which successfully couple to and from the tap fibers

SUMMARY OF THE INVENTION

It is accordingly an object of the invention to provide asymmetricmulti-mode fiber optic couplers which exhibit better coupling propertiesthan those hitherto produced.

The invention accordingly provides a method of fabricating an asymmetricmulti-mode fiber optic coupler comprising assembling the coupler fromtwo or more multi-mode optical fibers of different core and claddingdiameters but substantially equal cladding refractive indices, andwherein the fibers are selected so as to have substantially equaleffective refractive indices for their respective highest order claddingmodes, at least in the fabricated coupler.

The invention further provides an asymmetric multi-mode fiber opticcoupler having at least four optical fiber branches of at least twodifferent core and cladding diameters but substantially equal claddingrefractive indices, wherein the fiber branches further havesubstantially equal effective refractive indices for their respectivehighest order cladding modes. In one embodiment, the invention affords acoupler fabricated by the aforedescribed method.

If the cladding refractive indices of the fibers are not similar, highorder core modes of the fiber having the lower cladding refractive indexwill be unable to couple to corresponding core modes of the other fiberand will be lost. By matching the cladding refractive indices and theeffective refractive index of the highest cladding modes, the effectiverefractive index of each core mode of each fiber will lie above thecladding refractive index but below the core refractive index of theother fiber. Equilibration of n_(e) 's in both fibers is required tominimize the coupler excess loss and maximize the mode coupling betweenthe fibers in the coupling region.

In order to fabricate an asymmetric multi-mode fiber optic couplerhaving a predetermined or predictable power coupling factor, the methodof the invention preferably further includes selecting the opticalfibers in regard to their numerical apertures NA, and theircore-to-cladding radii ratios ρ_(co) /ρ_(cl) and subjecting the fibersto respective taper ratios T, so that, on assembly of the fibers to formthe coupler, the products ##EQU1## for the respective fibers are atleast momentarily equal, and wherein the assembly is thereuponcompleted.

In one embodiment, the values of NA and ρ_(co) /ρ_(cl) differ for therespective fibers and one of the fibers is subjected to a pretaperingbefore the fibers are drawn and thereby tapered together, whereby thevalues of T vary for the fibers in a manner to ensure equality of saidproducts

According to another embodiment, the optical fibers further have similarpeak core refractive indices. Two fibers of different core diametersformed in similar material, e.g. silica, generally have a similarcladding refractive index (that for doped silica) but quite differentpeak core refractive indices and this difference prevents or at leastsubstantially diminishes proper coupling of significant core modes inputon any branch of a coupler formed from the fibers In particular,important lower order modes input on a main branch (i.e., the widerfiber) will have effective refractive indices above the refractive indexof the tap branch and be unable to couple to the core of the tap branchas a general rule, the peak core refractive indices of commercialoptical fibers increase with core diameter. This is a naturalconsequence of the depositing technique by which the fiber cores areformed and of the resultant parabolic refractive index profile acrossthe core cross-section.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary graphical expression of the relationship of thevarious parameters at different α₁ values for α₂ =2.0.

FIG. 2A is a diagrammatic representation of STEP (A) of a manufacturingprocess in connection with preferred embodiment of the presentinvention.

FIG. 2B is a diagrammatic representation of STEP (B) of a manufacturingprocess in connection with a preferred embodiment of the presentinvention.

FIG. 2C is a diagrammatic representation of STEP (C) of a manufacturingprocess in connection with a preferred embodiment of the presentinvention.

FIG. 2D is a diagrammatic representation of STEP (D) of a manufacturingprocess in connection with a preferred embodiment of the presentinvention.

FIG. 2E is a diagrammatic representation of STEP (E) of a manufacturingprocess in connection with a preferred embodiment of the presentinvention.

FIG. 2F is a diagrammatic representation of STEP (F) of a manufacturingprocess in connection with a preferred embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

When optical fibers of different core diameters are formed in likematerial, e.g. silica cladding and a germanium-doped silica core, therequirement of equal peak cladding and equal peak core refractiveindices will typically be met when the fibers have equal numericalapertures It is known that the numerical aperture of an optical fiber isdependent on the level of doping in the core, e.g. germanium doping of asilica core.

For silica optical fibers, the numerical aperture (NA) is preferably inthe range 0.2 to 0.5. A higher NA, i.e. in this range, is generallydesirable because losses at a bend in an optical fiber decrease withincreasing numerical aperture

The coupler may be any of several known types, e.g. fused biconicaltaper couplers, polished couplers, couplers draw down in an outerwrapping, and drawn down twin-core couplers However, the coupler ispreferably a fused biconical coupler. In this case, however, it is foundthat even when using optical fibers of similar core refractive indicesand similar cladding refractive indices, significant higher order coremodes of one of the fibers, which should couple to the core of the otherfiber, are lost. In accordance with a second aspect of the invention, ithas been appreciated that this effect arises from the tapering step inthe coupler fabrication process and must be countered by properselection and/or preparation of fibers.

There are two limits in quantifying the power coupling factor t,depending on assumptions about the behavior of modes in the coupler. Ifevery mode of the coupler traverses the length of the taper purelyadiabatically, then there is no coupling between coupler modes If thenumerical aperture of one fiber entering the coupler is filled, therewill be equal excitation of all the modes of the other fiber which havea common effective index. For example, suppose the fibers have the samenumerical aperture and the main or bus fiber supports N₁ modes and thetap-off or branch fiber N₂ modes, with N₁ (N2. There are N₂ modes of thebus fiber which will share power with the N₂ modes of the tap-off fiber.Accordingly the tap-off ratio is (1/2 N₂ /N₁). Similarly, the N₂ modesof the tap-on fiber will share their power with N₂ modes of the busfiber, so that the tap-on ratio is 1/2. Furthermore, the wrap-aroundratio is also 1/2.

In a wholly non-adiabatic coupler, on the other hand, every mode coupleswith every other mode. This means that whatever the power distributionentering the coupler, it will be shared equally between all modesleaving the coupler Thus, for the two fibers discussed above, if the busfiber is excited, the power in its N₁ modes is shared between the N₁ +N₂modes of the coupler. In this case the tap-off ratio must be N₂ /{N₁ +N₂}. Similarly, the tap-on ratio is given by N₁ /{N₁ +N₂ }, and thewrap-around ratio is equal to the tap-off ratio.

A practical coupler is neither purely adiabatic nor non-adiabatic.Neither can there be complete coupling between all modes, since couplersare etched to minimize coupling between core and cladding modes, whichmust also minimize coupling between the highest-order core modes.Furthermore, as the tapering increases, coupling between all core modesdecreases.

Accordingly, the achievable tap-off and tap-on ratios in practicalcouplers will be bounded, in a sense, by the values for purely adiabaticand non-adiabatic couplers. However, it is found that real behavior isnearer the non-adiabatic limit.

Accordingly, for fabricating an asymmetric multi-mode fiber opticcoupler having a predetermined or predictable power coupling factor, themethod of the invention further includes selecting the ratio of the corediameters from a first range determined by a first inequality dependentupon said power coupling factor and upon the refractive index profilesof the fiber cores, and selecting the ratio of the cladding diametersfrom a second range determined by a second inequality dependent upon thepower coupling factor but independent of the core diameters and therefractive index profiles.

Advantageously, the coupler is a fused biconical taper fiber opticcoupler formed by heating said segments of the fibers while thesesegments are in intimate side-by-side contact to a temperaturesufficient to cause the fiber segments to fuse together, andlongitudinally drawing the heated fibers to cause each of the fusedfiber segments to develop a biconical taper and so form a coupler.

The optical fiber segments may be segments of respective optical fibersor the method may further include the step of etching one or both of twooptical fibers to reduce the cladding diameter(s) to achieve therequired ratio.

Both the ratio of the core diameters and the ratio of the claddingdiameters may be proportional to the square root of the power couplingfactor, with a constant of proportionality of (2)1/2, but the corediameter ratio is typically further proportional to a complex factor ofthe refractive index profile. More particularly, for the most commonclass of refractive index profiles, the α profiles, defined by:

    n.sub.2 (r)=n.sub.co.sup.2 [1-2Δ(r/ρ).sup.α }(1)

where n(r) is the refractive index at radial distance r from the coreaxis, n_(co) is the peak core refractive index, ρ is the core radius,and Δ is the relative index difference given by

    2Δ=1-(n.sub.cl /n.sub.co).sup.2                      (2)

where n_(cl) is the cladding refractive index, the power coupling factoris a power tap-off coupling factor t from a main or bus fiber to a tapor branch fiber, and said first inequality is the following, or anequivalent: ##EQU2## the main or bus fiber is indicated by subscript 1and the tap or branch fiber by subscript 2, and λ is the free spacewavelength of a prescribed source.

Where the numerical apertures of the fibers are substantially equal, thefirst and second inequalities may be the following, or equivalents:##EQU3##

It can also be demonstrated that the tap-on ratio t_(ON) for this coreis given by: ##EQU4##

In the above inequalities, the left-hand limit corresponds to theadiabatic case and the right-hand limit to the non-adiabatic case. Theleft-hand and right-hand sides of (3) are only equal if ρ_(co)2=ρ_(col), i.e. the cores are of equal diameter.

It will be appreciated that where the two fibers have similar corerefractive index profiles, s₁ =s₂ and expressions (3) and (4) become thesame and the requirement is for the ratio of the core diameters to equalthe ratio of the cladding diameters. It will also be appreciated thatexpressions (3) and (4) sustain one degree of freedom, viz the ratio ofcore to cladding diameters This may typically be determined by otherconsiderations such as minimum bending loss, fiber rigidity and soforth.

In the practical coupler, the highest-order modes are marginallyadiabatic and lower-order modes are certainly non-adiabatic. Thissuggests that, in the above inequalities, the practically achievablefigures for the various ratios are primarily governed by non-adiabaticbehavior. In practice then, where a specific power coupling factor isrequired, the inequalities above are used to select fiber parametersrelatively close to the non-adiabatic limit, and the resultant couplertested for any necessary adjustment.

The invention, in its further aspect, also provides an asymmetricmulti-mode fiber optic coupler having a predetermined power couplingfactor, formed from two or more multi-mode optical fibers of differentcore and cladding diameters but substantially equal cladding refractiveindices, wherein the fibers further have substantially equal effectiverefractive indices for their respective highest order cladding modes,and wherein the ratio of the core diameters is selected in dependenceupon said power coupling factor and upon the refractive index profilesof the fiber cores and the ratio of the cladding diameters is selectedin dependence upon the power coupling factor but is independent of thecore diameters and the refractive index profiles.

An exemplary pair of optical fiber segments for the case of similar corerefractive index profiles have respective diameters of 200 and 250micron and respective cladding diameters of 50 and 62.5 micron, a commonratio of 0.8. The former is commercially available; the latter may beproduced by etching a length of commercial optical fiber of corediameter 50 micron and cladding diameter 125 micron. This selectionresults in a coupler exhibiting 95% on-bus coupling between the main orbus branches, i.e. the larger diameter branches, about 1.5% coupling busto tap branch, and about 80% coupling tap branch to bus.

It is considered that, with asymmetric couplers fabricated according tothe principles of the invention, buses or networks of 50 or more tapsare quite feasible in view of the lower level of core mode and powerlosses achieved compared with prior asymmetric couplers Typicalelectronic buses which may now be directly implemented in optical fiberinclude IEEE802.3 and IEEE802.4.

The ratio of the core radius to outer cladding radius is preferablyselected to achieve a predetermined minimum power loss in the fibertaper regions and core waist regions of the subsequent coupler .The corewaist regions of the coupler are the reduced diameter portions of thecores between their tapers For this purpose, the ratio is preferably inthe range 0 6 to 0.8, most preferably between 0.67 and 0.77.

Said etching may be effected by immersing the fiber segments in a bathof a suitable acid, for example hydrofluoric acid, for a predeterminedtime.

The optical fiber segments are preferably brought into said side-by-sideintimate contact by being twisted about each other The segments areadvantageously initially under tension when being heated.

Said heating and drawing steps are preferably carried out in accordancewith international patent application No. PCT/AU87/00374 , utilizingapparatus also disclosed therein The method may also incorporate theprinciples disclosed in international patent application No.PCT/AU87/00380.

It is now proposed to detail the mathematical derivation of expressions(3) and (4).

For convenience, we assume that the core profiles belong to the class ofα profiles, defined by equation (1) above:

    n.sup.2 (r)=n.sub.co.sup.2 [1-2Δ(r/ρ.sub.co).sup.α ](1)

over the core 0<r<ρ_(co), where α >0, r is the radial distance from thefiber axis, ρ_(co) is the core radius, and Δ is the relative indexdifference given by equation (2) above:

2Δ1-(n_(cl) /n_(co))² (2)

The number of bound modes supported by a multi-mode fiber with one ofthese profiles is given by [7]: ##EQU5## where V is the normalizedfrequency, defined by: ##EQU6## and λ is the free-space wavelength ofthe source. If we introduce a "mode-number" parameter s into equation(6): ##EQU7## then, e.g. s=1/2 for the step profile (α=∞) and s=1/4 forthe parabolic profile (α=2).

Let t be the fraction of power coupled to the tap-off fiber from thethroughput fiber. The number of bound modes in the throughput andtap-off fibers is N₁ and N₂ respectively. As the throughput fiber islarger than the tap-off fiber, N₁ >N₂. Under purely adiabaticconditions, only N₂ modes couple and, consequently, the fraction ofpower coupling between the two fibers is N₂ /N₁. Since a large number ofmodes is involved, the coupled power will be split equally in the exitports. Hence the fraction of tap-off power is: ##EQU8## If we substitute(7) and (5) into (8) and denote the mode-number parameter and thenormalized frequency for the throughput and tap-off fibers by s₁, V₁,and s₂, V₂, respectively, then: ##EQU9## This is the left-hand side ofinequality (3).

In the particular case where the two fibers have the same numericalaperture, it follows from (5) that the ratio of normalized frequenciesis given by the corresponding ratio of core radii or diameters Thus:##EQU10## where 2ρ_(col) and 2ρ_(co2) are the core diameters of thethroughput and tap-off fibers respectively.

This is the left-hand side of inequality (3a) above.

For non-adiabatic behavior, where mixing between modes is complete,power is shared between N₁ +N₂ modes.

Thus the tap-off ratio is: ##EQU11## Substituting (7) and (5) into (8'):##EQU12## This is the right-hand side of inequality (3).

The number of modes in each fiber is proportional to the square of thecore sizes and the mode number parameter s. Then, again taking the casewhere both fibers have the same numerical aperture: ##EQU13##

This is the right-hand side of inequality (3a).

Accordingly equations (10) and (10') define the adiabatic andnon-adiabatic power tap-off coupling factors respectively such that in apractical situation the actual tap-off coupling factor is given byinequality (3) or (3a).

During tapering, the effective indices of the highest order modes--thosewith effective indices closest to the cladding index before tapering--must remain identical in the two fibers. Tapering "squeezes"high-order modes from the cores into the cladding, but the total numberof excited modes in the core and cladding of the tapered fiber mustequal the number of core modes before tapering.

Let T be the taper ratio, defined as: ##EQU14##

Mass conservation during tapering requires that T has the same value forthe core and cladding diameters of both the throughput and tap-offfibers As we showed above, the initial number of modes N_(is)proportional to the square of core radius, thus, if N(T) denotes thenumber of modes remaining in the core at taper ratio T, then:

    N(T)=N/T.sup.2                                             (12)

provided N(T)>>1.

Let N_(cl) (T) the number of modes squeezed into the cladding at taperratio T. If ρ_(cl) is the cladding radius of the untapered fiber, thenthe radius of the tapered fiber is ρ_(cl) /T. Accordingly, the number ofmodes in the cladding is equal to the number of modes on a step-profilefiber of diameter 2ρ_(cl) /T and numerical aperture (n_(cl) ² -n_(e)²)^(1/2), where n_(e) is the effective index of the highest-ordercladding mode. By analogy with the number of modes in the core of astep-profile fiber, N=V² /2, we have: ##EQU15## Invariance of the totalnumber of modes requires:

    N=N(T)+N.sub.cl (T)                                        (14)

Substituting from (5) and (12): ##EQU16##

If we substitute for V from (8) and for N_(cl) (T) from (13), andsimplify:

    2s(T.sup.2 -1)(n.sub.co.sup.2 -n.sub.cl.sup.2)ρ.sub.co.sup.2 =(n.sub.cl.sup.2 -n.sub.e.sup.2) ρ.sub.cl.sup.2       (16)

so that on rearranging:

    ne.sup.2 =n.sub.cl.sup.2 -2s(T.sup.2 -1)NA.sup.2 ×(ρ.sub.co ρ.sub.cl).sup.2                                       (17)

where NA (the numerical aperture)=(n_(co) ² -n_(cl) ²)1/2

It can be seen from this expression (17) that, where the n_(cl) valuefor the two fibers is substantially equal and their refractive indexprofile is of the α class (in which case S₁ =S₂), the requirement n_(el)=n_(e2) is met where the products ##EQU17## are equal. In the simple andtypical case where the T values are equal, equality of the effectiveindices of the highest order modes during tapering requires that theratio NA /(ρ_(cl) /ρ_(co) } be the same for both fibers.

The requirement that the n_(e) 's for the two fibers be identical forall taper ratios is obtained from (15) by setting s=s₁, ρ_(co) =ρ_(col),ρcl=ρ_(cl1) and NA=NA₁ for the throughput fiber, and s=s₂, ρ_(co)=ρ_(co2), ρ_(cl2) and NA=NA₂ for the tap-off fiber, all other quantitieshaving common values This leads to: ##EQU18## which relates thecore-diameter ratio to the cladding-diameter ratio.

On rearranging (10), the adiabatic case, the core diameter of thetap-off fiber is related to the core diameter of the throughput fiberby: ##EQU19##

If we eliminate the ratio of core diameters from (18) and rearrange:

    2ρ.sub.cl2 =2ρ.sub.cl1 (2t).sup.1/2                (20)

which is equivalent to the left-hand side of inequality (4a) above. Itwill be noted that the ratio of the cladding diameters of the two fibersis independent of the core diameters and refractive index profiles.

On rearranging (10'), the non-adiabatic case ##EQU20## substitute from(18) and rearranging gives: ##EQU21## which is the equivalent of theright-hand side of inequality (4a) above. Again, the ratio of thecladding diameters of the two fibers is independent of the corediameters and refractive index profiles.

Some particular cases will now be exemplified.

1. Identical Core Profiles

If the core profiles have the same shape, e.g. both step or bothparabolic, then s₁ =s₂ and ##EQU22## in (19) (20) (19') and (20'), sothat the cladding and core diameters are in the same proportion.

2. Parabolic Core (Throughput) & Step Core Tap-Off)

In this case α, is very large and α2=2. Equation (15) gives s₁ =1/4 ands₂ =1/2, whence (19) and (20) reduce to:

    2ρ.sub.co2 2ρ.sub.col t.sup.1/2 ;2ρ.sub.cl2 =2ρ.sub.cl1 (2t).sup.1/2

so that the core of the tap-off fiber is relatively smaller than thecladding, consistent with the larger number of modes on thestep-profile.

3. Step Core (Throughout) & Parabolic Core (Tap-Off)

We now have s₁ 1/2and S₂ =1/4, so that (19) and (20) give:

    2ρ.sub.co2 =2ρ.sub.col (4t).sup.1/2 ;2ρ.sub.cl2 =2ρ.sub.cl1 (2t).sup.1/2

so that the core of the tap-off fiber is relatively larger than thecladding, consistent with the smaller number of modes on the parabolicprofile.

Utilizing expressions (3a) and (4a), given the tap-off ratio, then allthe core and cladding diameters of the two fibers are prescribed, withthe exception of the ratio of cladding-to-core diameters for one of thefibers, which then uniquely determines this ratio for the other Fiber.In other words, there is one degree of freedom remaining, which will bedetermined by other considerations, such as bending loss, fiberrigidity, etc.

The limits for inequalities (4a) were determined above for equal T andNA values In a more general case, equation (17) may be utilized toobtain a predetermined or predictable power coupling factor where the NAand ρ_(co) /ρ_(cl) values for the fibers are quite different It is stillrequired that n_(el) =n_(e2) and equation (17) then indicates that theproducts ##EQU23## should be equal, assuming n_(cl) are equal.

If one of the fibers is pretapered, the dissimilarity in NA and ρ_(co)/ρ_(cl) ratio can be balanced, at least at one point in thedrawing/tapering process, by creating a dissimilarity between the Tvalues.

By way of example, an asymmetric coupler is made from fibers havingrespective ρ_(co) /ρ_(cl) ratios of 208/250 and 100/140. The former isetched to 208/210 and latter to 100/105 only the smaller fiber is thenpretapered to 67/70. The two fibers are twisted, fused and drawn in theknown manner. According to equation (17), and using x for the ratio##EQU24## For 208/210 etched fiber x=0.157 T² =1=15 at completion oftapering Thus the product (T₂ -1)x is x(T² -1)=2.36For 100/105 etchedfiber x=0.0763Pretapered to 67/70 T² -1=30.4 at completion of tapering.

Thus the product is x. (T² -1)=2.32

Thus, at the completion of fiber tapering when the required coupling isachieved, and the original taper ratio of the bus fiber is the same asin previous couplers not subject to this technique, the products of xand T² -1 are essentially equal, so that the n_(e) 's for both fibersare equal Note that the n_(e) 's are not equal throughout the whole ofthe tapering process. They are equal at only one moment, and it is theability to predict this moment as the moment when the required opticalperformance occurs that is provided by equation (17).

It will be appreciated that equation (17) may be applied to predict thenominal optical performance of two fibers assembled into a coupler, orto design and construct an asymmetric coupler of normal opticalperformance from two fibers of arbitrary dimensions and opticalparameters.

It is thus important to appreciate that the concepts enunciated in theabove mathematical exposition are not confined to the special casesdiscussed herein i.e. similar peak core and cladding refractive indices,a particular family of refractive index profiles and biconical tapercouplers In particular, equations (8), (9), (16) and (17) have generalapplication and the invention in its most general aspects provides amethod of designing and/or forming a fiber optic coupler in accordancewith these equations and their precursors and derivatives.

FIG. 1 is an exemplary graphical expression of the relationship of thevarious parameters at different α₁ values for α₂ = 2.0. The followingtwo examples indicate how the graph, or like graphs for othercircumstances, may be employed.

A. Given α₁ /α₂ and the core ratio between the fibers proceed asfollows:

1. Locate core ratio on vertical axis.

2. Draw horizontal line and intersect appropriate α₁ /α₂ curve.

3. Draw vertical line from this intersection to horizontal split ratioaxis.

4. This is the maximum split ratio for the coupler.

5. Note the intersection of the vertical line with the α₁ /α₂ =1 curve.

6. Draw a horizontal line to the vertical axis.

7. This gives the cladding ratio for the two fibers.

Note the large fiber is always the main fiber, and the smaller fiber thetap.

B. Conversely, given any split ratio and α₁ /α₂ :

1. Draw a vertical line to the intersection of α₁ /α₂ =1.0 curve.

2. This intersection gives cladding ratio.

3. Continue the vertical line to intersect the appropriate α/α curve.

4. This intersection gives the core ratio.

The invention will now be further described, by way of an exemplaryembodiment only, with reference to the accompanying diagrams depictingthe principal physical steps of a preferred method of actuallyfabricating fibers once the fibers have been selected in accordance withthe invention, showing the form of the optical fibers at the conclusionof each step. In this exemplary embodiment, for simplicity, theadiabatic limit is selected as satisfactory. Two lengths 10,11 ofoptical fiber, for example multi-mode silica fiber with agermanium-doped core 26, are first stripped of their outer protectivecoating 14 in respective portions 12, 13 (STEP A.). Fiber 10 is to bethe bus fiber in the subsequent coupler and has a core radius r₁ of 100micron and an outer cladding radius r₂ of 125 micron, a ratio of 0.8.The desired power coupling ratio is 1%, so fiber 11, which is to formthe tap fiber, has a core radius r₁ of 36 micron (as required by theleft-hand side of inequality (3)) and an outer cladding radius r₂ of 38micron. The numerical aperture for each fiber is: NA₁ =0.4 and NA₂=0.27. The parabolic core refractive index profiles are characterizedby: α₁ =3.1 and α₂ is 2.0, with S₁ =0.61 and S₂ =0.25.

Fiber portion 13 is immersed in a bath of, for example, hydrofluoricacid at say, ambient temperature to etch the silica cladding 25 within asegment 17 and so increase the ratio of core radius to outer claddingradius to a value equal to that as required by expressions (3) and (4),(STEP B). Residence time in the bath is generally dependent on the exactnature of the acid employed, but might be significantly reduced byemploying hot and/or flowing acid.

The two fibers are then laid parallel about 0.5 to 1.0 mm apart by beingheld in a pair of clamps 18, 20 so that the segment 17 and a matchingsegment 16 of fiber portion 12, extend under tension side-by-side (STEPC.). One clamp 18 is rotated to twist the fiber segments together inintimate side-by-side contact (STEP D.). The intimately contacted andinitially tensioned fiber segments are then heated sufficiently tosoften and fuse the fibers together to form a join 30 (STEP E.).

To cause the cores 26 to form respective biconical tapers 23, the fibersare longitudinally drawn equally and oppositely, and the coupler iscomplete (STEP F.). It may now be packaged and/or encapsulated by knownmethods to render it resistant to hostile environments as well as robustand shock resistant. During drawing, the radii of core and cladding bothdiminish considerably but their ratio remains substantially constant.

In an actual example in close conformity with the above exemplaryembodiment, the final values of core and cladding radii r₁ and r₂ werefound to be 16 microns and 22 microns respectively for the bus branchesand 8 microns and 12 microns respectively for the tap branches. Thetap-off power coupling factor was measured and observed to be 0.08, veryclose to the desired factor of 0.1. The tap-on power coupling factor was0.70.

We claim:
 1. A method of fabricating an asymmetric multi-mode fiberoptic coupler comprising assembling the coupler from two or moremulti-mode optical fibers of different core and cladding diameters butsubstantially equal cladding refractive indices, and wherein the fibersare selected so as to have substantially equal effective refractiveindices for their respective highest-order cladding modes, at least inthe fabricated coupler.
 2. A method according to claim 1 for fabricatingan asymmetric multi-mode fiber optic coupler having a predetermined orpredictable power coupling factor, wherein said optical fibers areselected in regard to their numerical apertures NA, and theircore-to-cladding radii ratios ρ_(co) /ρ_(cl) and subjected to respectivetaper ratios T so that, on assembly of the fibers to form the coupler,the products ##EQU25## for the respective fibers are at leastmomentarily equal.
 3. A method according to claim 1 or 2 wherein saidoptical fibers further have similar peak core refractive indices.
 4. Amethod according to claim 3 wherein said optical fibers are formed inlike material and of similar numerical aperture, whereby to have saidsimilar cladding and peak core refractive indices.
 5. A method accordingto claim 4 wherein said optical fibers are silica optical fibers andhave substantially identical numerical apertures in the range 0.2 to0.5.
 6. A method according to claim 1 or 2 for fabricating an asymmetricmulti-mode fiber optic coupler having a predetermined or predictablepower coupling factor, wherein the ratio of the core diameters isselected from a first range determined by a first inequality dependentupon said power coupling factor and upon the refractive index profilesof the fiber cores, and the ratio of the cladding diameters is selectedfrom a second range determined by a second inequality dependent upon thepower coupling factor but independent of the core diameters and therefractive index profiles.
 7. A method according to claim 6 wherein thelimits of said inequalities are determined by strict adiabatic andnon-adiabatic behavior respectively, and the said selections are maderelatively close to the non-adiabatic limit.
 8. A method according toclaim 6 for fabricating a fused biconical taper fiber optic coupler,wherein both the ratio of the core diameters and the ratio of thecladding diameters are proportional to the square root of the powercoupling factor, with a constant of proportionality of (2)^(1/2), butthe core diameter ratio is typically further proportional to a complexfactor of the refractive index profile.
 9. A method according to claim 8wherein the optical fibers exhibit refractive index profiles, the αprofiles, defined by:

    n.sup.2 (r)=n.sub.co.sup.2 [1-2Δ(r/ρ).sup.α ]

wherein n(r) is the refractive index at radial distance r from the coreaxis, n_(co) is the peak core refractive index, ρ is the core radius, αis a parameter indicative of the particular refractive index profile,and Δ is the relative index difference given by

    Δ= - (n.sub.cl /n.sub.co).sup.2

wherein n_(cl) is the cladding refractive index, the power couplingfactor is a power tap-off coupling factor t from a main or bus fiber toa tap or branch fiber, and said first inequality is the following, or anequivalent: ##EQU26## the main or bus fiber is indicated by subscript 1and the tap or branch fiber by subscript 2, and λ is the free spacewavelength of a prescribed source.
 10. A method according to claim 9wherein the numerical apertures of the fibers are substantially equaland said first and second inequalities are the following, or equivalents##EQU27##
 11. A method according to claim 2 including the steps ofheating said segments of the fibers while these segments are in intimateside-by-side contact to a temperature sufficient to cause the fibersegments to fuse together, and longitudinally drawing the heated fibersto cause each of the fused fiber segments to develop a biconical taperand so form a coupler.
 12. A method according to claim 2 wherein thevalues of NA and ρ_(co) /ρ_(pl) differ for the respective fibers and oneof the fibers is subjected to a pretapering before the fibers are drawnand thereby tapered together, whereby the values of T vary for thefibers in a manner to ensure equality of said product.
 13. An asymmetricmulti-mode fiber optic coupler fabricated by the method of claim
 2. 14.An asymmetric multi-mode fiber optic coupler fabricated by the method ofclaim
 1. 15. An asymmetric multi-mode fiber optic couPler having atleast four optical fiber branches of at least two different core andcladding diameters but substantially equal cladding refractive indices,wherein the fiber branches further have substantially equal effectiverefractive indices for their respective highest order cladding modes.